Related papers: Degeneration at $E_2$ of Certain Spectral Sequence…

For a regular function f on a smooth complex quasi-projective variety, J.-D. Yu introduced in arXiv:1203.2338 a filtration (the irregular Hodge filtration) on the de Rham complex with twisted differential d+df, extending a definition of…

The aim of the paper is to introduce an alternative notion of two-scale convergence which gives a more natural modeling approach to the homogenization of partial differential equations with periodically oscillating coefficients: while…

On a compact $\partial\bar\partial$-manifold $X$, one has the Hodge decomposition: the de Rham cohomology groups split into subspaces of pure-type classes as $H_{dR}^k (X)=\oplus_{p+q=k}H^{p,\,q}(X)$, where the $H^{p,\,q}(X)$ are…

We prove mixed-characteristic analogues of the Connes and Feigin--Tsygan degeneration theorem. Let $W=W(k)$ be the Witt vectors of a perfect field of characteristic $p>0$. For a smooth proper variety $X$ over $W$, the de Rham-to-$\HP$…

In this paper, we develop $L^2$ theory for Riemannian and Hermitian foliations on manifolds with basic boundary. We establish a decomposition theorem, various vanishing theorems, a twisted duality theorem for basic cohomologies and an…

We consider degenerate elliptic equations of second order in divergence form with a symmetric random coefficient field $a$. Extending the work of the first author, Fehrman, and Otto [Ann. Appl. Probab. 28 (2018), no. 3, 1379-1422], who…

We study half-line Schr\"odinger operators with locally $H^{-1}$ potentials. In the first part, we focus on a general spectral theoretic framework for such operators, including a Last--Simon-type description of the absolutely continuous…

Let $(X,h)$ be a compact and irreducible Hermitian complex space of complex dimension $m$. In this paper we are interested in the Dolbeault operator acting on the space of $L^2$ sections of the canonical bundle of $reg(X)$, the regular part…

This is a revised version of ANT-0049. Given an elliptic curve E --> B over a base B with zero section i, we denote, letting E':= E - i(B), by L(E) the Q-vector space with basis ({s}, s \in E'(B)). Assume that B is smooth and separated over…

The goal of this note is to prove that Hodge-de Rham degeneration holds for smooth and proper $\mathbf{F}_p$-schemes $X$ with $\dim(X)<p^n$ as soon as its category of quasicoherent sheaves admits a lift to the truncated Brown-Peterson…

Let (M,I, \omega, \Omega) be a nearly Kaehler 6-manifold, that is, an SU(3)-manifold with the (3,0)-form \Omega and the Hermitian form \omega which satisfies $d\omega=3\lambda\Re\Omega, d\Im\Omega=-2\lambda\omega^2$, for a non-zero real…

We introduce a notion of ellipticity of complexes of linear pseudodifferential operators acting on sections of $A$-Hilbert bundles over smooth manifolds, $A$ being a $C^*$-algebra. We prove that the cohomology groups of an $A$-elliptic…

In this paper we show that a notion of non-degeneracy which allows to develop Morse theory is generically satisfied for a large class of $C^2$-functionals defined on Banach spaces. The main element of novelty with respect to the previous…

Double forms are sections of the vector bundles $\Lambda^{k}T^*\mathcal{M}\otimes \Lambda^{m}T^*\mathcal{M}$, where in this work $(\mathcal{M},\mathfrak{g})$ is a compact Riemannian manifold with boundary. We study graded second-order…

On Riemannian signature conformal 4-manifolds we give a conformally invariant extension of the Maxwell operator on 1-forms. We show the extension is in an appropriate sense injectively elliptic, and recovers the invariant gauge operator of…

We investigate connections between the sGG property of compact complex manifolds, defined in earlier work by the second author and L. Ugarte by the requirement that every Gauduchon metric be strongly Gauduchon, and a possible degeneration…

Given an autonomous second-order ordinary differential equation (ODE), we define a Riemannian metric on an open subset of the first-order jet bundle. A relationship is established between the solutions of the ODE and the geodesic curves…

For essential reduced hyperplane arrangements of 4 variables, we show that the pole order spectral sequence degenerates almost at $E_2$, and completely at $E_3$, generalizing the 3 variable case where the complete $E_2$-degeneration is…

We study the effect of quantum corrections on heterotic compactifications on elliptic fibrations away from the stable degeneration limit, elaborating on a recent observation by Malmendier and Morrison. We show that already for the simplest…

The paper deals with the asymptotic behavior as $\eps\to 0$ of the spectrum of Laplace-Beltrami operator $\Delta\e$ on the Riemannian manifold $M\e$ ($\mathrm{\dim} M\e=N\geq 2$) depending on a small parameter $\eps>0$. $M\e$ consists of…